What is the value of (cos(pi/6))/((1-sin(pi/6))^2) ?

The value of (cos(pi/6))/((1-sin(pi/6))^2) is 2sqrt(3)

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(cos(pi/6))/((1-sin(pi/6))^2)

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

23

Solution steps

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{\frac{3}{2}}{( 1 - \frac{1}{2} ) ^{2}}

Simplify

\frac{\frac{3}{2}}{( 1 - \frac{1}{2} ) ^{2}} : 23

= 23

arctan (\frac{5}{15})

cos (12 9^{\circ})

sech^{2} (1)

3 arctan (\frac{1}{7}) + 2 arctan (\frac{2}{11})

arcsin (sin (1 7^{\circ}))

What is the value of (cos(pi/6))/((1-sin(pi/6))^2) ?
The value of (cos(pi/6))/((1-sin(pi/6))^2) is 2sqrt(3)